Abstract

The Neurospora biorhythm model is based on the negative feedback auto regulation of gene expression. This research is about the comparative mathematical model for Neurospora process which specific effects on light only and on light with the FRQ protein. The models are analyzed by a differential equation theory, to find equilibrium points, the stability and the limit cycle state. The Routh-Hurwitz criterion is used for finding the parameters that confirm each state. Besides, we can verify all values of the parameters by using numerical method and solution curves.

Citation details of the article

Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 30
Issue: 1
Year: 2017

DOI: 10.12732/ijam.v30i1.5

Download Section

Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

1. [1] W.E. Boyce, R.C. Diprima, Elementary Differential Equations and Boundary Value Problem, John Wiley Inc., New Jersey (2004).
2. [2] S.K. Crosthwaite, J.C. Dunlap, J.J. Loros, Neurospora wc-1 and wc-2: Transcription, photoresponses, and the origins of circadian rhythmicity, Science, 276 (1997), 763-769.
3. [3] S.K. Crosthwaite, J.J. Loros, J.C. Dunlap, Light-induced resetting ofcircadian clock is mediated by a rapid increase in frequency transcript, Cell, 81 (1995), 1003-1012.
4. [4] J.C. Dunlap, Genetic and molecular analysis of circadian rhythms, Annu. Rev. Genet., 30 (1996), 579-601.
5. [5] A. Goldbeter, Biochemical Oscillations and Cellular Rhythms: The Molecular Bases of Periodic and Chaotic Behaviour, Cambridge University Press, Cambridge (1996).
6. [6] A.T. Winfree, The Geometry of Biological Time, Springer, New York (1980).
7. [7] B.C. Goodwin, Oscillatory behavior in enzymatic control processes, Adv. Enzyme Regul., 3 (1965), 425-438.
8. [8] K. Drescher, G. Cornelius, L. Rensing, Phase response curves obtained by perturbing different variables of a 24 hr model oscillator based on translational control, J. Theor. Biol., 94 (1982), 345-353.
9. [9] D. Gonze, J.C. Leloup, A. Goldbeter, Theoretical model for circadian rhythms in Neurospora and Drosophila, C. R. Acad. Sci. Life Sciences, 323 (2000), 57-67.
10. [10] H. Tei, H. Okamura, Y. Shigeyoshi, C. Fukuhara, R. Ozawa, M. Hirose, Y. Sakaki, Circadian oscillation of a mammalian homologue of the Drosophila period gene, Nature, 389 (1997), 512-516.
11. [11] B.D. Aronson, K.A. Johnson, J.J. Loros, J.C. Dunlap, Negative feedback defining a circadian clock: Autoregulation of the clock gene frequency, Science, 263 (1994), 1578-1584.
12. [12] M. Hunter-Ensor, A. Ousley, A. Sehgal, Regulation of the Drosophila protein timeless suggests a mechanism for resetting the circadian clock by light, Cell, 84 (1996), 677-685.
13. [13] C. Lee, V. Parikh, T. Itsukaichi, K. Bae, I. Edery, Resetting the Drosophila clock by photic regulation of PER and a PER-TIM complex, Science, 271 (1996), 1740-1744.
14. [14] M.P. Myers, K. Wager-Smith, A. Rothenfluh-Hilfiker, M.W. Young, Lightinduced degradation of TIMELESS and entrainment of the Drosophila circadian clock, Science, 271 (1996), 1736-1740.
15. [15] H. Zeng, Z. Qian, M.P. Myers, M. Rosbash, A light-entrainment mechanism for the Drosophila circadian clock, Nature, 380 (1996), 129-135.
16. [16] D. Gonze, J.C. Leloup, A. Goldbeter, Theoretical models for circadianrhythms in Neurospora and Drosophila, C.R. Acad. Sci. Paris. Sciences de la vie/Life Sciences, 323 (2000), 57-67.
17. [17] K. Kumnungkit, N. Wongvisetsirikul, Neurospora Biorhythm mathematical model with light-dark cycle, In: Proceeding of 6th IMT-GT Conference on Mathematics, Statistics and its Applications, ICMSA2010 (2010), 809821.
18. [18] K. Kumnungkit, S. Suwannaut, Effective Neurospora process model on light and FRQ protein, In: Proceeding of 6th IMT-GT Conference on Mathematics, Statistics and its Applications, ICMSA2010 (2010), 796-808.